There's no real way to show steps taken to equate "the better to ..." and "so as to ... better", since the construction isn't easily generalized - for example, "the faster to run" or "the bigger to grow" doesn't really sound natural (edited since my original examples were bad)

English also has phrases like "the more, the merrier" where all the verbs and nouns are dropped and only adjectives are left, maybe acting like nouns at that point. In your example @PLTR PSTH "the better" seems to be used as an adjective, even though "the" indicates that "better" is a noun. Probably another case of "flexible word order" meets "aggressive elision". In your example I can say "he leaned closer, into the better position to hear her" ... but, I cannot generalize that example.